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Topic: Spider´s data and the Jarque-Bera test
Replies: 1   Last Post: Feb 24, 2013 4:38 PM

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Luis A. Afonso

Posts: 4,617
From: LIsbon (Portugal)
Registered: 2/16/05
Spider´s data and the Jarque-Bera test
Posted: Feb 24, 2013 11:11 AM
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Spider´s data and the Jarque-Bera test
Concerning each random variable, S, k, JB the following procedure was used. By S0, k0, JB0 was denoted the Skewness, Excess kurtosis and Jarque-Bera observed values in data.
a) By Monte Carlo simulations a large number M of normal samples n size pseudo-samples was obtained, the mean and standard deviation equal to those the real sample show,
b) From each one S was calculated. The M set of values play the role of Null Hypotheses to which S0 will be compared,
c) Then the number of times S>S0 is counted, the total divided by M assimilated to the parameter´s p-value.
The same treatment for the Excess Kurtosis and female spider´s data leads to:

____Female____________________Male_____
______sample mean = 8.127__________5.917
______________sd = 1.134__________0.663
______S=Skewness = 1.0269_________1.0181
__k=_Exc. Kurtosis = -1.9287________-1.9512
______________ JB = 9.922_________ 9.942

___p-values by Monte Carlo simulations:
____ S, k, JB observed < normal model
Criterium: if normal frequency > obsv. value : count
(see my post: Sep 10 2012 7:03 PM)

___________S = 0.0044____________0.0450
___________k = 1.0000____________1.0000
__________JB = 0.0004____________0.0004

Conclusion
In what concerns JB-LM statistics, the results do reject that samples were drawn from normal Populations.
arxiv.org/pdf/math/0509423 .
Critical values:
5%, 2.8814(n=35), 2.3417(n=30) ;1%, 11.736, 8.7182
Because 100% simulated k are larger than both samples observed values, it leads to persuade that both male and female lengths are platikurtic.

Luis A. Afonso



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